Subgroups — ((C₅⋊D₅)⋊C₃)⋊D₁₀₉ #45658267

Order 32700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₉⋊#3874	C₂	1	2	yes	maximal, complemented
3	(C₅⋊D₅)⋊D₁₀₉	—	3	1	no	maximal, Hall
4	C₅²⋊C₃×C₁₀₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅⋊D₅×C₁₀₉	D₃	1	1	yes	characteristic, complemented
6	C₅×D₅₄₅	—	3	2	no	—
7	C₅²×C₁₀₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	D₅×D₁₀₉	—	15	2	no	—
9	C₂×D₃₂₇	—	25	1	no	maximal, Hall
10	D₅₄₅	—	3	2	no	—
11	C₅×D₁₀₉	—	15	2	no	—
12	D₅×C₁₀₉	—	15	2	no	—
13	C₂×C₃×C₁₀₉	—	25	1	no	—
14	D₃₂₇	—	25	2	no	—
15	C₅×C₁₀₉	—	3	2	no	—
16	C₂×D₁₀₉	—	75	1	no	Hall
17	C₃×C₁₀₉	—	25	1	no	Hall
18	#3874⋊C₂	—	109	1	no	maximal, Hall
19	C₂×C₁₀₉	—	25	1	no	—
20	D₁₀₉	—	15	2	no	—
21	(C₅⋊D₅)⋊C₃	D₁₀₉	1	1	yes	characteristic, complemented
22	#3874	—	109	2	no	—
23	C₁₀₉	#3874⋊C₂	1	1	yes	characteristic, complemented, Sylow
24	D₅²	—	327	1	no	Hall
25	C₅²⋊C₃	C₂×D₁₀₉	1	1	yes	characteristic, complemented, Hall
26	C₅⋊D₅	D₃₂₇	1	1	yes	characteristic, complemented
27	C₅×D₅	—	327	2	no	—
28	C₅²	C₂×D₃₂₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×D₅	—	1635	2	no	—
30	C₂×D₃	—	2725	1	no	Hall
31	C₂×C₅	—	1635	2	no	—
32	D₅	—	15	2	no	—
33	D₅	—	327	2	no	—
34	C₂×C₃	—	25	1	no	—
35	D₃	—	2725	2	no	—
36	C₅	—	3	2	no	—
37	C₂²	—	8175	1	no	Sylow
38	C₃	—	25	1	no	Sylow
39	C₂	—	25	1	no	—
40	C₂	—	1635	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅²⋊C₃×C₁₀₉	C₂²
Fitting, socle	C₅²×C₁₀₉	C₂×D₃
LCS	G ▷ C₅²⋊C₃×C₁₀₉
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.